Multiscale method for simulating two and three-phase flow in porous media

Abstract

Multiscale methods developed to solve coupled flow equations for reservoir simulation are based on a hierarchical strategy in which the pressure equation is solved on a coarsened grid and transport equation is solved on the fine grid as a decoupled system. The multiscale mixed finite-element (MsMFE) method attempts to capture sub-grid geological heterogeneity directly into the coarse-scale via mathematical basis functions. These basis functions are able to capture important multiscale information and are coupled through a global formulation to provide good approximation of the subsurface flow solution.In the literature, the general formulation of the MsMFE method for incompressible two-phase and compressible three-phase flow has mainly addressed problems with idealized flow physics. In this paper, we present a new formulation that accounts for compressibility, gravity, and spatially-dependent capillary and relative-permeability effects.We evaluate the computational efficiency and accuracy of the method by reporting the result of series of representative benchmark tests that have a high degree of realism with respect to flow physics, heterogeneity in petrophysical model, and geometry/topology of the corner-point grids. In particular, the MsMFE method is validated and compared against Shell's in-house simulator MoReS. The fine-scale flux, pressure, and saturation fields computed by the multiscale simulation show a noteworthy improvement in resolution and accuracy compared with coarse-scale models.

A Multiscale Method Based on Restriction-Smoothed Basis Functions Suitable for General Grids in High Contrast Media

“…The resulting method can efficiently predict two-phase flow patterns that are qualitatively correct for highly heterogeneous and geologically complex reservoir models Natvig et al 2011;Alpak et al 2012;Pal et al 2013). The method has also been extended towards realistic flow physics (Krogstad et al 2009, but this has proved difficult to achieve in a fully robust manner because of the inherent assumption of a pressure equation written on mixed form.…”